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I'd like to know if this type of construction has a name, and for that matter, if it's even grammatically correct. I can remember seeing it in certain formal texts, but not as much recently:
The dog began to growl, despite his continuing to wag his tail.
She still held out hope for good news, as shown by her checking the mail each morning.
Those are made-up; I can't find a good real-life example right now. But the way I explain it is that a continuous action like "checking the mail each morning" is made into a noun-like object and treated as a possession of a person. It seems somewhat stiff, and in most cases I think you could rewrite the sentence to use more direct phrasing. But is it valid? And what is it called?